Solution to a Linear System in a General Matrix in Banded Storage (Simple Driver)

Calling Sequence

CALL DGBSV	(N, NSUB, NSUPER, NRHS, DA, LDA, IPIVOT, DB, LDB, INFO)
CALL SGBSV	(N, NSUB, NSUPER, NRHS, SA, LDA, IPIVOT, SB, LDB, INFO)
CALL ZGBSV	(N, NSUB, NSUPER, NRHS, ZA, LDA, IPIVOT, ZB, LDB, INFO)
CALL CGBSV	(N, NSUB, NSUPER, NRHS, CA, LDA, IPIVOT, CB, LDB, INFO)
void dgbsv	(int n, int nsub, int nsuper, int nrhs, double *da, int lda, int *ipivot, double *db, int ldb, int *info)
void sgbsv	(int n, int nsub, int nsuper, int nrhs, float *sa, int lda, int *ipivot, float *sb, int ldb, int *info)
void zgbsv	(int n, int nsub, int nsuper, int nrhs, doublecomplex *za, int lda, int *ipivot, doublecomplex *zb, int ldb, int *info)
void cgbsv	(int n, int nsub, int nsuper, int nrhs, complex *ca, int lda, int *ipivot, complex *cb, int ldb, int *info)

Arguments

N	Order of the matrix A. N 0.
NSUB	Number of subdiagonals of A. N-1 NSUB 0 but if N = 0 then NSUB = 0.
NSUPER	Number of superdiagonals of A. N-1 NSUPER 0 but if N = 0 then NSUPER = 0.
NRHS	Number of right-hand sides, equal to the number of columns in the matrix B. NRHS 0.
xA	On entry, the matrix A stored in rows NSUB+1 through 2 × NSUB + NSUPER + 1. Rows 1 through NSUB are ignored on entry and do not need to be set. On exit, the LU factorization of the matrix A as computed by xGBTRF.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA 2 × NSUB + NSUPER + 1.
IPIVOT	Pivot indices as computed by xGBTRF.
xB	On entry, the N×NRHS right-hand side matrix B. On exit, the N×NRHS solution matrix X.
LDB	Leading dimension of the array B as specified in a dimension or type statement. LDB max(1, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	U(i,i), where i = INFO, is exactly zero and U is therefore singular. The LU factorization has been completed, but the solution could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDAB, LDAG, LDB, N, NRHS, NSUB, NSUPER

INTEGER SIZEAB, SIZEB

PARAMETER (NSUB = 1)

PARAMETER (NSUPER = 1)

PARAMETER (N = 4)

PARAMETER (NRHS = 1)

PARAMETER (LDAB = 2*NSUB + NSUPER + 1)

PARAMETER (LDAG = N)

PARAMETER (LDB = N)

PARAMETER (SIZEAB = LDAB * N)

PARAMETER (SIZEB = LDB * NRHS)

C

DOUBLE PRECISION AB(LDAB,N), AG(LDAG,N), B(LDB,NRHS)

INTEGER ICOL, INFO, IPIVOT(N), IROW, IROWB, I1, I2

INTEGER M

C

EXTERNAL DGBSV

INTRINSIC MAX0, MIN0

C

C Initialize the array AG to store the 4x4 matrix A with one

C subdiagonal and one superdiagonal shown below. Initialize

C the array B to store the vector b shown below.

C

C 2 -1 5

C AG = -1 2 -1 b = 5

C -1 2 -1 5

C -1 2 5

C

DATA AB / SIZEAB*8.0D8 /

DATA AG / 2.0D0, -1.0D0, 2*0.0, -1.0D0, 2.0D0, -1.0D0,

$ 0.0D0, 0.0D0, -1.0D0, 2.0D0, -1.0D0, 2*0D0,

$ -1.0D0, 2.0D0 /

DATA B / SIZEB*5.0D0 /

C

C Copy the matrix A from the array AG to the array AB. The

C matrix is stored in general storage mode in AG and it will

C be stored in banded storage mode in AB. The code to copy

C from general to banded storage mode was written for LINPACK

C by Cleve Moler.

C

M = NSUB + NSUPER + 1

DO 20, ICOL = 1, N

I1 = MAX0 (1, ICOL - NSUPER)

I2 = MIN0 (N, ICOL + NSUB)

DO 10, IROW = I1, I2

IROWB = IROW - ICOL + M

AB(IROWB,ICOL) = AG(IROW,ICOL)

10 CONTINUE

20 CONTINUE

C

C Print the initial values of the arrays.

C

PRINT 1000

PRINT 1010, ((AG(IROW,ICOL), ICOL = 1, N), IROW = 1, N)

PRINT 1020

PRINT 1010, ((AB(IROW,ICOL), ICOL = 1, N), IROW = 1, LDAB)

PRINT 1030

PRINT 1040, B

C

C Solve the system Ax=b.

C

CALL DGBSV (N, NSUB, NSUPER, NRHS, AB, LDAB, IPIVOT,

$ B, LDB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1050

PRINT 1040, B

ELSE

PRINT 1060, INFO

END IF

C

1000 FORMAT (1X, 'A in full form:')

1010 FORMAT (4(3X, F4.1))

1020 FORMAT (/1X, 'A in banded form: (* in unused elements)')

1030 FORMAT (/1X, 'b:')

1040 FORMAT (1X, 2X, F4.1)

1050 FORMAT (/1X, 'x:')

1060 FORMAT (1X, 'Error in solving system, INFO = ', I3)

C

END

Sample Output

A in full form:
2.0 -1.0 0.0 0.0
-1.0 2.0 -1.0 0.0
0.0 -1.0 2.0 -1.0
0.0 0.0 -1.0 2.0
A in banded form: (* in unused elements)
**** **** **** ****
**** -1.0 -1.0 -1.0
2.0 2.0 2.0 2.0
-1.0 -1.0 -1.0 ****
b:
5.0
5.0
5.0
5.0
x:
10.0
15.0
15.0
10.0